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1

Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations

Raissi, M., Perdikaris, P., Karniadakis, G.E.

Journal:

Journal of Computational Physics

Year:

2018

Language:

english

File:

PDF, 2.23 MB

english, 2018

2

Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations

Raissi, Maziar, Karniadakis, George Em

Journal:

Journal of Computational Physics

Year:

2017

Language:

english

File:

PDF, 4.23 MB

english, 2017

3

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

Raissi, Maziar, Yazdani, Alireza, Karniadakis, George Em

Journal:

Year:

2020

Language:

english

File:

PDF, 2.80 MB

english, 2020

4

fPINNs: Fractional Physics-Informed Neural Networks

Pang, Guofei, Lu, Lu, Karniadakis, George Em

Journal:

SIAM Journal on Scientific Computing

Year:

2019

Language:

english

File:

PDF, 1.14 MB

english, 2019

5

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

Xiu, Dongbin, Karniadakis, George Em

Journal:

SIAM Journal on Scientific Computing

Year:

2002

Language:

english

File:

PDF, 439 KB

english, 2002

6

NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

Jin, Xiaowei, Cai, Shengze, Li, Hui, Karniadakis, George Em

Journal:

Journal of Computational Physics

Year:

2020

File:

PDF, 5.39 MB

2020

7

[Lecture Notes in Computational Science and Engineering] Discontinuous Galerkin Methods Volume 11 || The Development of Discontinuous Galerkin Methods

Cockburn, Bernardo, Karniadakis, George E., Shu, Chi-Wang

Year:

2000

Language:

english

File:

PDF, 5.53 MB

english, 2000

8

Modeling of blood flow in arterial trees

Tomer Anor, Leopold Grinberg, Hyoungsu Baek, Joseph R. Madsen, Mahesh V. Jayaraman, George E. Karniadakis

Journal:

Wiley Interdisciplinary Reviews: Systems Biology and Medicine

Year:

2010

Language:

english

File:

PDF, 689 KB

english, 2010

9

REPORT: A MODEL FOR FLOWS IN CHANNELS, PIPES, AND DUCTS AT MICRO AND NANO SCALES

Ali Beskok, George Em Karniadakis,

Journal:

Microscale Thermophysical Engineering

Year:

1999

Language:

english

File:

PDF, 540 KB

english, 1999

10

Deep learning of vortex-induced vibrations

Raissi, Maziar, Wang, Zhicheng, Triantafyllou, Michael S., Karniadakis, George Em

Journal:

Journal of Fluid Mechanics

Year:

2019

Language:

english

File:

PDF, 699 KB

english, 2019

11

Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems

Jagtap, Ameya D., Kharazmi, Ehsan, Karniadakis, George Em

Journal:

Computer Methods in Applied Mechanics and Engineering

Year:

2020

File:

PDF, 20.94 MB

2020

12

B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

Yang, Liu, Meng, Xuhui, Karniadakis, George Em

Journal:

Journal of Computational Physics

Year:

2020

File:

PDF, 5.31 MB

2020

13

High-order splitting methods for the incompressible Navier-Stokes equations

George Em Karniadakis, Moshe Israeli, Steven A Orszag

Journal:

Journal of Computational Physics

Year:

1991

Language:

english

File:

PDF, 1.42 MB

english, 1991

14

DNS of flow past a stationary and oscillating cylinder at

S. Dong, G.E. Karniadakis

Journal:

Journal of Fluids and Structures

Year:

2005

Language:

english

File:

PDF, 696 KB

english, 2005

15

Fractional Sturm–Liouville eigen-problems: Theory and numerical approximation

Zayernouri, Mohsen, Karniadakis, George Em

Journal:

Journal of Computational Physics

Year:

2013

Language:

english

File:

PDF, 1.44 MB

english, 2013

16

Rarefaction and Compressibility Effects in Gas Microflows

Beskok, Ali, Karniadakis, George Em, Trimmer, William

Journal:

Journal of Fluids Engineering

Year:

1996

Language:

english

File:

PDF, 1.15 MB

english, 1996

17

[ASME ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference - Honolulu, Hawaii, USA (July 6–10, 2003)] Volume 1: Fora, Parts A, B, C, and D - Vortex-Induced Vibrations of Long Marine Risers in Sheared Flows: DNS Studies

Lucor, Didier, Ma, X., Triantafyllou, M. S., Karniadakis, G. E.

Year:

2003

Language:

english

File:

PDF, 2.98 MB

english, 2003

18

Parametric Gaussian process regression for big data

Raissi, Maziar, Babaee, Hessam, Karniadakis, George Em

Journal:

Computational Mechanics

Year:

2019

Language:

english

File:

PDF, 2.02 MB

english, 2019

19

hp-VPINNs: Variational physics-informed neural networks with domain decomposition

Kharazmi, Ehsan, Zhang, Zhongqiang, Karniadakis, George E.M.

Journal:

Computer Methods in Applied Mechanics and Engineering

Year:

2021

File:

PDF, 8.78 MB

2021

20

A new triangular and tetrahedral basis for high-order (hp) finite element methods

Spencer J. Sherwin, George Em Karniadakis

Journal:

International Journal for Numerical Methods in Engineering

Year:

1995

Language:

english

File:

PDF, 1.33 MB

english, 1995

21

Equation-free/Galerkin-free POD-assisted computation of incompressible flows

Sirod Sirisup, George Em Karniadakis, Dongbin Xiu, Ioannis G. Kevrekidis

Journal:

Journal of Computational Physics

Year:

2005

Language:

english

File:

PDF, 1.55 MB

english, 2005

22

Recent advances in parallel spectral element simulation of unsteady incompressible flows

Paul F. Fischer, Ho Lee-Wing, George E. Karniadakis, Einar M. Rønouist, Anthony T. Patera

Journal:

Computers & Structures

Year:

1988

Language:

english

File:

PDF, 1.47 MB

english, 1988

23

Three-dimensional dynamics and transition to turbulence in the wake of bluff objects

Karniadakis, George Em, Triantafyllou, George S.

Journal:

Journal of Fluid Mechanics

Year:

1992

Language:

english

File:

PDF, 6.12 MB

english, 1992

24

[Lecture Notes in Computational Science and Engineering] Discontinuous Galerkin Methods Volume 11 ||

Cockburn, Bernardo, Karniadakis, George E., Shu, Chi-Wang

Year:

2000

Language:

english

File:

PDF, 397 KB

english, 2000

25

Second-order approximations for variable order fractional derivatives: Algorithms and applications

Zhao, Xuan, Sun, Zhi-zhong, Karniadakis, George Em

Journal:

Journal of Computational Physics

Year:

2015

Language:

english

File:

PDF, 427 KB

english, 2015

26

A phase-field method for 3D simulation of two-phase heat transfer

Zheng, X., Babaee, H., Dong, S., Chryssostomidis, C., Karniadakis, G.E.

Journal:

International Journal of Heat and Mass Transfer

Year:

2015

Language:

english

File:

PDF, 2.44 MB

english, 2015

27

Tempered Fractional Sturm--Liouville EigenProblems

Zayernouri, Mohsen, Ainsworth, Mark, Karniadakis, George Em

Journal:

SIAM Journal on Scientific Computing

Year:

2015

Language:

english

File:

PDF, 289 KB

english, 2015

28

Spectral/hp Element Methods for Computational Fluid Dynamics || ALGORITHMS FOR INCOMPRESSIBLE FLOWS

Karniadakis, George, Sherwin, Spencer

Year:

2005

Language:

english

File:

PDF, 115 KB

english, 2005

29

111 years of Brownian motion

Bian, Xin, Kim, Changho, Karniadakis, George Em

Journal:

Year:

2016

Language:

english

File:

PDF, 2.27 MB

english, 2016

30

Spectral/hp Element Methods for Computational Fluid Dynamics || FUNDAMENTAL CONCEPTS IN ONE DIMENSION

Karniadakis, George, Sherwin, Spencer

Year:

2005

Language:

english

File:

PDF, 114 KB

english, 2005

31

Inferring solutions of differential equations using noisy multi-fidelity data

Raissi, Maziar, Perdikaris, Paris, Karniadakis, George Em

Journal:

Journal of Computational Physics

Year:

2017

Language:

english

File:

PDF, 1.68 MB

english, 2017

32

[Applied Mathematical Sciences] Numerical Methods for Stochastic Partial Differential Equations with White Noise Volume 196 || Numerical schemes for SDEs with time delay using the Wong-Zakai approximation

Zhang, Zhongqiang, Karniadakis, George Em

Year:

2017

Language:

english

File:

PDF, 788 KB

english, 2017

33

[Applied Mathematical Sciences] Numerical Methods for Stochastic Partial Differential Equations with White Noise Volume 196 || Stochastic collocation methods for differential equations with white noise

Zhang, Zhongqiang, Karniadakis, George Em

Year:

2017

Language:

english

File:

PDF, 383 KB

english, 2017

34

A partitioned coupling framework for peridynamics and classical theory: Analysis and simulations

Yu, Yue, Bargos, Fabiano F., You, Huaiqian, Parks, Michael L., Bittencourt, Marco L., Karniadakis, George E.

Journal:

Computer Methods in Applied Mechanics and Engineering

Year:

2018

Language:

english

File:

PDF, 3.29 MB

english, 2018

35

Stochastic Domain Decomposition via Moment Minimization

Zhang, Dongkun, Babaee, Hessam, Karniadakis, George Em

Journal:

SIAM Journal on Scientific Computing

Year:

2018

Language:

english

File:

PDF, 3.98 MB

english, 2018

36

Correction to: A computational mechanics special issue on: data-driven modeling and simulation—theory, methods, and applications

Liu, Wing Kam, Karniadakis, George, Tang, Shaoqiang, Yvonnet, Julien

Journal:

Computational Mechanics

Year:

2019

Language:

english

File:

PDF, 134 KB

english, 2019

37

A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

Meng, Xuhui, Karniadakis, George Em

Journal:

Journal of Computational Physics

Year:

2019

File:

PDF, 1.26 MB

2019

38

What Is the Fractional Laplacian? A Comparative Review with New Results

Lischke, Anna, Pang, Guofei, Gulian, Mamikon, Song, Fangying, Glusa, Christian, Zheng, Xiaoning, Mao, Zhiping, Cai, Wei, Meerschaert, Mark M., Ainsworth, Mark, Karniadakis, George Em

Journal:

Journal of Computational Physics

Year:

2019

Language:

english

File:

PDF, 8.51 MB

english, 2019

39

Physics-informed neural networks for high-speed flows

Mao, Zhiping, Jagtap, Ameya D., Karniadakis, George Em

Journal:

Computer Methods in Applied Mechanics and Engineering

Year:

2020

File:

PDF, 3.06 MB

2020

40

Predictability and uncertainty in CFD

D. Lucor, D. Xiu, C.-H. Su, G. E. Karniadakis

Journal:

International Journal for Numerical Methods in Fluids

Year:

2003

Language:

english

File:

PDF, 571 KB

english, 2003

41

Numerical Simulation of the Ion Etching Process

S.J. Sherwin, G.E. Karniadakis, S.A. Orszag

Journal:

Journal of Computational Physics

Year:

1994

File:

PDF, 1.18 MB

1994

42

A Discontinuous Galerkin Method for the Viscous MHD Equations

T.C Warburton, G.E Karniadakis

Journal:

Journal of Computational Physics

Year:

1999

Language:

english

File:

PDF, 673 KB

english, 1999

43

A Spectral Vanishing Viscosity Method for Large-Eddy Simulations

G-S. Karamanos, G.E. Karniadakis

Journal:

Journal of Computational Physics

Year:

2000

Language:

english

File:

PDF, 729 KB

english, 2000

44

SIMULATIONS OF FLOW OVER A FLEXIBLE CABLE: A COMPARISON OF FORCED AND FLOW-INDUCED VIBRATION

D. Newman, G.E. Karniadakis

Journal:

Journal of Fluids and Structures

Year:

1996

Language:

english

File:

PDF, 1.11 MB

english, 1996

45

Numerical simulation of forced convection heat transfer from a cylinder in crossflow

George EM Karniadakis

Journal:

International Journal of Heat and Mass Transfer

Year:

1988

Language:

english

File:

PDF, 928 KB

english, 1988

46

Spectral element-Fourier methods for incompressible turbulent flows

G.E. Karniadakis

Journal:

Computer Methods in Applied Mechanics and Engineering

Year:

1990

Language:

english

File:

PDF, 1.21 MB

english, 1990

47

Spectral element simulations of laminar and turbulent flows in complex geometries

George Em Karniadakis

Journal:

Applied Numerical Mathematics

Year:

1989

Language:

english

File:

PDF, 930 KB

english, 1989

48

Multi-element probabilistic collocation method in high dimensions

Jasmine Foo, George Em Karniadakis

Journal:

Journal of Computational Physics

Year:

2010

Language:

english

File:

PDF, 1021 KB

english, 2010

49

Modeling electrokinetic flows by the smoothed profile method

Xian Luo, Ali Beskok, George Em Karniadakis

Journal:

Journal of Computational Physics

Year:

2010

Language:

english

File:

PDF, 1.21 MB

english, 2010

50

Time-dependent generalized polynomial chaos

Marc Gerritsma, Jan-Bart van der Steen, Peter Vos, George Karniadakis

Journal:

Journal of Computational Physics

Year:

2010

Language:

english

File:

PDF, 5.46 MB

english, 2010

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